Some Issues In The Loop Variable Approach to Open Strings and an Extension to Closed Strings

TL;DR

This paper examines the loop variable renormalization group approach to open and closed string gauge invariance, highlighting its unique features, constraints, and connection to the Virasoro algebra, with extensions to closed strings.

Contribution

It introduces a novel perspective on gauge invariance in string theory using the loop variable approach, including an extension from open to closed strings.

Findings

The approach yields a simple gauge transformation law.

The theory resembles a higher-dimensional massless theory with dimensional reduction.

Extensions to closed strings are straightforward.

Abstract

Some issues in the loop variable renormalization group approach to gauge invariant equations for the free fields of the open string are discussed. It had been shown in an earlier paper that this leads to a simple form of the gauge transformation law. We discuss in some detail some of the curious features encountered there. The theory looks a little like a massless theory in one higher dimension that can be dimensionally reduced to give a massive theory. We discuss the origin of some constraints that are needed for gauge invariance and also for reducing the set of fields to that of standard string theory. The mechanism of gauge invariance and the connection with the Virasoro algebra is a little different from the usual story and is discussed. It is also shown that these results can be extended in a straightforward manner to closed strings.